Asource of information randomly generates symbols from a four letter alphabet {w, x, y, z }. the probability of each symbol is as follows: p(w) = 1 2 ; p(x) = 1 4 ; p(y) = 1 8 ; and p(z) = 1 8 . these symbols are now encoded into binary codes using the scheme shown below. let the random variable l denote the length of the binary code and pl(l) denote the pmf of l. symbol codew 0x 10y 110z 111find the expectation and variance of l.

Rectangle leg this 11feet and perimeter of 38feet what is the width of the rectangle in feet

Qrst is a parallelogram. determine the measure of ∠q pls

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)